Finite Group Databasebeta

← C2×#13080001 #15626643

Subgroups — C2×#13080001 #15626643

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic, complemented
2C2×#10623247C211yesmaximal, characteristic
3#13080001C2116yesmaximal, direct product factor
4C2×#10622463C211yesmaximal, characteristic, complemented
5C2×#10622634C211yesmaximal, characteristic, complemented
6C2×#10622372C212yesmaximal, complemented
7C2×#10622393C212yesmaximal, complemented
8C2×#10622787C212yesmaximal, complemented
9C2×#10622688C211yesmaximal, characteristic, complemented
10C2×#10622775C212yesmaximal, complemented
11C2×#10622450C211yesmaximal, characteristic, complemented
12C2×C11×#460C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C22×C11×SD16C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19C2×#66991—21no—
20C2×#66991C2212yes—
21C2×#66989—21no—
22C2×D4×Dic11—21no—
23C2×D4×Dic11C2212yes—
24C22×#4324C2212yes—
25C22×#4313C2212yes—
26#10623247—24no—
27#10623247C2218yes—
28#10623109—24no—
29#10623109C2218yescomplemented
30C2×#66950C2211yescharacteristic
31C2×#66949—21no—
32C2×#66942—21no—
33C2×#66941C2211yescharacteristic
34C2×#66925—21no—
35C2×C42×D11C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C2×C4×Dic22—21no—
38C2×C4×Dic22C2211yescharacteristic
39C11×#460C2218yescomplemented
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#102C2212yes—
42C2×#66899C2212yes—
43C2×#66896C2212yes—
44#10622787C22116yescomplemented
45#10622775C22116yescomplemented
46C2×#66882C2212yes—
47C2×#66880C2212yes—
48C2×Dic11⋊C8C2212yes—
49#10622688C2218yescomplemented
50#10622634C2218yescomplemented
51C2×#66871C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622463C2218yescomplemented
54#10622450C2218yescomplemented
55#10622393C22116yescomplemented
56#10622372C22116yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11C2312yes—
61C22×C22⋊D11—22no—
62C23×Dic11—22no—
63C2×#4341—28no—
64C2×#4341—48no—
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×Dic22—21no—
69C22×Dic22—21no—
70C22×Dic22C2311yescharacteristic
71C2×C11×SD16—44no—
72C2×C11×SD16C2318yes—
73C22×C8×C11C2312yes—
74C11×#127—22no—
75C11×#127C2314yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84#66999—22no—
85#66999C2314yes—
86#66997—22no—
87#66997C2314yes—
88#66991—24no—
89#66991—28no—
90#66991C2318yes—
91#66989—28no—
92D4×Dic11—24no—
93D4×Dic11—28no—
94D4×Dic11C2318yes—
95C2×#4324—44no—
96C2×#4324C2318yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2312yes—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11D411yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2312yes—
113C2×#4313—44no—
114C2×#4313C2318yes—
115#66950—22no—
116#66950C2314yes—
117#66949—28no—
118#66942—28no—
119#66941—22no—
120#66941C2314yes—
121#66925—28no—
122C42×D11D414yes—
123C42×D11C2314yes—
124#66922—22no—
125#66922C2314yes—
126C4×Dic22—22no—
127C4×Dic22—28no—
128C4×Dic22C2314yes—
129C11×C4⋊C8C2314yes—
130C11×#102C2318yes—
131#66899C2318yes—
132#66896C2318yes—
133#66882C2318yes—
134#66880C2318yes—
135Dic11⋊C8C2318yes—
136#66871C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3254—111nomaximal, Sylow
139C24×C11—22no—
140C23×D11C2×D411yescharacteristic
141C2×Q8×C11—21no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11C2412yes—
145C2×D4×C11—22no—
146C2×D4×C11—24no—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—44no—
151C2×D4×C11—44no—
152C2×D4×C11C2414yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—28no—
159C2×C22⋊D11—48no—
160C22×Dic11—28no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—48no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168#4341—432no—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11C2×D412yes—
174C2×C4×D11C2×D414yes—
175C2×C4×D11C2×D414yes—
176C2×C4×D11C2412yes—
177C2×Dic22—24no—
178C2×Dic22—21no—
179C2×Dic22—24no—
180C2×Dic22—22no—
181C2×Dic22—22no—
182C2×Dic22—44no—
183C2×Dic22—44no—
184C2×Dic22C2412yes—
185C11×SD16—48no—
186C2×C8×C11—24no—
187C2×C8×C11C2414yes—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4C2412yes—
191C42×C11—24no—
192C42×C11C2×D412yes—
193C42×C11C2412yes—
194C22⋊Dic11—28no—
195C22⋊Dic11—28no—
196#4324—48no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199C4⋊Dic11—24no—
200C4⋊Dic11—21no—
201C4⋊Dic11—22no—
202C4⋊Dic11—24no—
203C4⋊Dic11C2414yes—
204C4⋊Dic11C2412yes—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210C4×Dic11—24no—
211C4×Dic11C2×D414yes—
212C4×Dic11C2×D412yes—
213C4×Dic11C2×D414yes—
214C4×Dic11C2412yes—
215C2×C11⋊C8—24no—
216C2×C11⋊C8C2414yes—
217#4313—48no—
218C2×#533—111no—
219C2×#532—111no—
220#3254—1116no—
221C2×#477—111no—
222C2×#477—111no—
223C2×#474—112no—
224C2×#468—112no—
225C2×#468—112no—
226C2×#460—111no—
227C2×#460D1111yescharacteristic, complemented
228C2×#461—112no—
229C2×#423—111no—
230C23×C11—24no—
231C23×C11—44no—
232C23×C11—44no—
233C23×C11—44no—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11C22×D412yes—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—42no—
242D4×C11—24no—
243D4×C11—24no—
244D4×C11—48no—
245D4×C11—44no—
246D4×C11—48no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11#13714yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C11H(5,𝔽2)12yes—
257C2×C4×C112−1+412yes—
258C2×C4×C11C2511yescharacteristic
259C22⋊D11—416no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—44no—
268C2×Dic11—416no—
269C2×Dic11AGL(1,ℤ/8)14yes—
270C2×Dic11C22×D412yes—
271C2×Dic11C22×D412yes—
272C2×Dic11C22×D412yes—
273C4×D11—24no—
274C4×D11—28no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—28no—
278Dic22—22no—
279Dic22—22no—
280Dic22—48no—
281Dic22—42no—
282Dic22—48no—
283C8×C11—24no—
284C11⋊C8—24no—
285C22×#41—221no—
286C22×SD16—112no—
287C22×SD16C2×D1112yes—
288C22×M16—112no—
289#533—118no—
290#533—224no—
291#532—118no—
292#532—224no—
293C2×C4⋊Q8—111no—
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8—111no—
296C2×#127C2×D1111yescharacteristic
297C2×#125—221no—
298C2×#124—221no—
299C2×C22⋊Q8—111no—
300C2×C22⋊Q8—111no—
301C2×C22⋊Q8—221no—
302C2×#121—112no—
303C2×#121—221no—
304C2×C4×Q8—111no—
305C2×C4×Q8—221no—
306C2×C4×Q8C2×D1111yescharacteristic
307C2×C4×D4—112no—
308C2×C4×D4—221no—
309C2×#117—221no—
310C22×C42—111no—
311#477—118no—
312#477—118no—
313#474—1116no—
314#468—1116no—
315#468—1116no—
316#461—1116no—
317#460—118no—
318#460C2×D1118yescomplemented
319C2×#107—112no—
320C2×#107—112no—
321#423—118no—
322C2×C4⋊C8—112no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8C2×D1111yescharacteristic
325C2×#103—112no—
326C2×#103—112no—
327C2×#102—112no—
328C2×#102C2×D1112yes—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—88no—
333C22×C11#53712yes—
334C22×C11C2×AGL(1,ℤ/8)12yes—
335C22×C11C2×#13712yes—
336C22×C11C23×D411yescharacteristic
337C2×D11—22no—
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—44no—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11#53712yes—
345C4×C11C2×#13714yes—
346C4×C11C2×H(5,𝔽2)11yescharacteristic
347C4×C11C2×2−1+411yescharacteristic
348Dic11—22no—
349Dic11—22no—
350Dic11—42no—
351Dic11—42no—
352Dic11—44no—
353Dic11C2×AGL(1,ℤ/8)14yes—
354C2×#41—228no—
355C2×#41—448no—
356C22×Q8—111no—
357C22×Q8—221no—
358C22×Q8—221no—
359C22×Q8C22×D1111yescharacteristic
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—222no—
363C22×D4C22×D1112yes—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—222no—
368C2×SD16—44no—
369C2×SD16—118no—
370C2×SD16—444no—
371C2×SD16C22×D1118yes—
372C2×M16—118no—
373C2×M16—444no—
374C22×C8—112no—
375C22×C8C22×D1112yes—
376C4⋊Q8—114no—
377C4⋊Q8—114no—
378C4⋊Q8—114no—
379C4⋊Q8—222no—
380C4⋊Q8—222no—
381C4⋊Q8—222no—
382#127—22no—
383#127C22×D1114yes—
384#125—228no—
385#124—228no—
386C22⋊Q8—114no—
387C22⋊Q8—114no—
388C22⋊Q8—222no—
389C22⋊Q8—228no—
390C22⋊Q8—222no—
391#121—118no—
392#121—224no—
393#121—228no—
394C4×Q8—22no—
395C4×Q8—114no—
396C4×Q8—228no—
397C4×Q8—222no—
398C4×Q8C22×D1114yes—
399C4×D4—118no—
400C4×D4—224no—
401C4×D4—228no—
402#117—228no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C42—21no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—114no—
423C2×C42—114no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426#107—118no—
427#107—118no—
428C4⋊C8—118no—
429C4⋊C8—114no—
430C4⋊C8C22×D1114yes—
431#103—118no—
432#103—118no—
433#102—118no—
434#102C22×D1118yes—
435C2×C11—84no—
436C2×C11#325414yescomplemented
437C2×C11C2×#53711yescharacteristic
438C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
439C2×C11C22×#13711yescharacteristic
440D11—42no—
441C24—22no—
442C24—111no—
443#41—4432no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—112no—
448C2×Q8—224no—
449C2×Q8—221no—
450C2×Q8—224no—
451C2×Q8—222no—
452C2×Q8—222no—
453C2×Q8—444no—
454C2×Q8—444no—
455C2×Q8C23×D1112yes—
456C2×D4—22no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—228no—
464C2×D4—448no—
465C2×D4C23×D1114yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—114no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—112no—
475C22×C4—224no—
476C22×C4—228no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—222no—
483C22×C4—448no—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487SD16—48no—
488SD16—448no—
489M16—448no—
490C2×C8—24no—
491C2×C8—114no—
492C2×C8—224no—
493C2×C8C23×D1114yes—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—112no—
497C4⋊C4—114no—
498C4⋊C4—224no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—222no—
504C4⋊C4—221no—
505C4⋊C4—224no—
506C4⋊C4—224no—
507C4⋊C4C23×D1112yes—
508C22⋊C4—224no—
509C22⋊C4—224no—
510C22⋊C4—228no—
511C22⋊C4—228no—
512C42—24no—
513C42—114no—
514C42—112no—
515C42—114no—
516C42—112no—
517C42—224no—
518C42D4×D1112yes—
519C42C23×D1112yes—
520C11C2×#325411yescharacteristic, complemented, Sylow
521C23—24no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—112no—
526C23—222no—
527C23—222no—
528C23—222no—
529C23C2×D4×D1111yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—42no—
533Q8—222no—
534Q8—222no—
535Q8—448no—
536Q8—448no—
537Q8—442no—
538D4—24no—
539D4—24no—
540D4—48no—
541D4—48no—
542D4—44no—
543D4—4416no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—114no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—228no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—228no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—4416no—
564C2×C4—444no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4#6696814yes—
568C2×C4C2×D4×D1112yes—
569C2×C4C2×D4×D1112yes—
570C2×C4C2×D4×D1111yescharacteristic
571C2×C4#6703712yes—
572C2×C4#6704312yes—
573C2×C4C24×D1111yescharacteristic
574C8—24no—
575C8—224no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—88no—
580C22—222no—
581C22—222no—
582C22—222no—
583C22—444no—
584C22#1062313912yes—
585C22C2×#6696812yes—
586C22D11×AGL(1,ℤ/8)12yes—
587C22C22×D4×D1111yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—114no—
592C4—222no—
593C4—222no—
594C4—442no—
595C4—444no—
596C4—442no—
597C4#1062313912yes—
598C4C2×#6696814yes—
599C4C2×#6703711yescharacteristic
600C4C2×#6704311yescharacteristic
601C2—84no—
602C2—442no—
603C2#1308000114yesdirect product factor
604C2C2×#1062313911yescharacteristic
605C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
606C2C22×#6696811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
prime radicalC2×#10623247C2
hypercenterC2×#460D11
hypocenterC11C2×#3254
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10623109C2semidirect
3. #13080001C2direct (N × H)
4. C2×#10622463C2semidirect
5. C2×#10622634C2semidirect
6. C2×#10622372C2semidirect
7. C2×#10622393C2semidirect
8. C2×#10622787C2semidirect
9. C2×#10622688C2semidirect
10. C2×#10622775C2semidirect
11. C2×#10622450C2semidirect
12. C2×C11×#460C2semidirect
29. #10623109C22semidirect
39. C11×#460C22semidirect
44. #10622787C22semidirect
45. #10622775C22semidirect
49. #10622688C22semidirect
50. #10622634C22semidirect
53. #10622463C22semidirect
54. #10622450C22semidirect
55. #10622393C22semidirect
56. #10622372C22semidirect
227. C2×#460D11semidirect
318. #460C2×D11semidirect
436. C2×C11#3254semidirect
520. C11C2×#3254semidirect
603. C2#13080001direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106231092
C2×#106232472
#130800012
C2×#106224632
C2×#106226342
C2×#106223722
C2×#106223932
C2×#106227872
C2×#106226882
C2×#106227752
C2×#106224502
C2×C11×#4602
C2×#325411